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Math Help - Normal distribution - please help ASAP! 3

  1. #1
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    Normal distribution - please help ASAP! 3

    5) Let Z be a standard normal random variable. Calculate each of the following:

    a. P(Z-1)
    b. P(-1.5 < Z < 1)
    c. P({-2 < Z < 0} OR {1 < Z 2})
    d. P({-2 < Z < 1} AND {0 < Z < 3})

    Thank you so much!
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  2. #2
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    Quote Originally Posted by MiyuCat View Post
    5) Let Z be a standard normal random variable. Calculate each of the following:

    a. P(Z-1)
    b. P(-1.5 < Z < 1)
    c. P({-2 < Z < 0} OR {1 < Z 2})
    d. P({-2 < Z < 1} AND {0 < Z < 3})

    Thank you so much!
    I suggest you review this material in your classnotes and textbook. I will show the approach for (b):

    Pr(-1.5 < Z < 1) = 1 - Pr(Z < -1.5) - Pr(Z > 1).

    Now note that Pr(Z > 1) = 1 - Pr(Z < 1) and Pr(Z < -1.5) = Pr(Z > 1.5) = 1 - Pr(Z < 1.5) by symmetry. Now use your tables to look up the values.
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  3. #3
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    For all of these problems use Z table - Normal Distribution

    Quote Originally Posted by MiyuCat View Post

    a. P(Z-1)
    Do you mean P(Z<-1) ?


    Quote Originally Posted by MiyuCat View Post

    b. P(-1.5 < Z < 1)
    This one becaomes P(Z<1)-P(Z<-1.5)

    Quote Originally Posted by MiyuCat View Post


    c. P({-2 < Z < 0} OR {1 < Z 2})

    This one makes no sense please re-post. The OR operator will indicate the whole region taken up by both inequalities.


    Quote Originally Posted by MiyuCat View Post


    d. P({-2 < Z < 1} AND {0 < Z < 3})
    The AND operator will indicate the whole region shared by both inequalities.

    Try P(0<Z<1)
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  4. #4
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    c. P({-2 < Z < 0} OR {1 < Z < 2})

    Sorry about that!

    And yes, I did mean P(Z > 1). Sorry again!

    Thanks a lot, you guys! A lot of help. We just started doing this and the professor doesn't explain it that well...
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